Problem solving week
Second class
Warm up
z
z
z
Explain to your group members how you got your
alternative solution to the pool border problem.
Write in your notes every question you were asked by
your group members about your solution.
To think about:
z Do
D you thi
think
k your answers convinced
i
d th
them th
thatt your
solution is correct?
z How would you verify that they understood your
solution?
P lb
Pool
border
d problem
bl
z
Solution we obtained to the pool border problem was
S+S+S+S+4
I can represent this on our
diagram as follows:
S
S
S
S
P lb
Pool
border
d problem
bl
z
Pictorially explain how each of these solutions was
obtained:
z
z
z
z
z
4(n+1)
4n+4
2n+2(n+2)
2n+2n+4
4(n+2)-4
My survey
z
“II want to learn how to teach math”
math
z
I want to have a solid understanding of math
concepts.
C
Comments
t
z
Calculators
z
Practicum
z
Portfolio
z
Work load
I t
Interesting
ti
number
b
z
The Indian mathematician Ramanujan observed that the
taxi number 1729 was very interesting because it was
the smallest counting number that could be expressed
as the sum off cubes in two different
ff
ways. Find the
numbers whose cubes added give you 1729.
St t i used?
Strategies
d?
• Trial and error
• Make a list of cubes
• Create a formula (to use in trial and error)
L k
Lakes
z
The surface of Big Lake is 31 feet above the
surface of Long Lake. Long lake is half as
deep as Big Lake and the bottom of Long
Lake is 8 feet below the bottom of Big Lake.
How deep is each lake?
St t i ?
Strategies?
•
•
•
•
Draw a picture
Make a list of what I know and what I need to know
Write an expression that corresponds to our situation
L b l
Label
P i t on a circle
Points
i l
z
If 20 points are placed on a circle and every pair of
points are joined with a segment, what is the total
number of segments drawn?
z
What if n points were placed on a circle?
Strategies used?
•Draw a picture
•Write an expression
•Count
•Look for pattern
•List
List
•Try a simpler case
Ti
Triangular
l numbers
b
z
The triangular numbers are the whole numbers
represented by certain triangular array of dots. The first
five triangular numbers are
z
z
z
z
z
Make a sketch to represent the seventh triangular
number.
How many dots will there be in the 10th triangular
number?
Is there a triangular number that has 150 dots in its
shape?
Write a formula for the number of dots in the nth
triangular
g
number.
Find the sum 1+2+3+4+ … +100
St t i used?
Strategies
d?
R i ?
Recipe?
z
Is there a recipe for solving problems?
z
z
No, but …
Is there a general outline one might use when
approaching the problem?
z
z
z
z
Make sure you understand the problem
Devise a plan
Carry it out
L kb
Look
back
k
St t i
Strategies
z
z
z
z
z
z
z
z
z
z
Guess and check
Draw a picture/diagram
Use a variable
Make a list
Look for a pattern
Solve a simpler problem
Use direct reasoning
Work backwards
Use cases
Look for a formula ……
O
Ongoing
i
assignment
i
t
On the course wiki we will develop Problem solving document. As you are
solving problems, give your strategy a name and list with it when you think this
may be a good strategy to use together with an example that you used it for.
Example:
STRATEGY
z
Draw a picture/diagram
CLUES
• Geometric figures are involved
• We can visually represent the
problem
• There are measurements given
Come back and add clues and strategies.
Come back and look for inspiration if you get stuck on a problem
problem.
Password is : elmath
Individual work – cookie jar
problem
bl
There is a jar with cookies on the table. Amanda walked in
and ate halff since she hadn’t had breakfast
f
that morning.
Rodney walked in afterwards and took a third of what was
left over. Natalie was going to her next class, noticed the
cookies and decided to take fourth of them with her. Jerilee
dashed in and grabbed a cookie to munch on. When Jamie
looked into the jar there were only two left. “How many
cookies were there to begin with?” she asked.